[1907.03452] Deep splitting method for parabolic PDEs
In this paper we introduce a numerical method for nonlinear parabolic PDEs that combines operator splitting with deep learning. It divides the PDE approximation problem into a sequence of separate learning problems. Since the computational graph for each of the subproblems is comparatively small, the approach can handle extremely high-dimensional PDEs. We test the method on different examples from physics, stochastic control and mathematical finance. In all cases, it yields very good results in up to 10,000 dimensions with short run times.
Deep splitting method for parabolic PDEs Christian Beck1, Sebastian Becker2, Patrick Cheridito3, Arnulf Jentzen4, and Ariel Neufeld5 arXiv:1907.03452v2 [math.NA] 21 Jun 2021 1 Department of Mathematics, ETH Zurich, Switzerland, e-mail: christian.beck@math.ethz.ch 2 Department of…
saved by
related reading
- Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learningarxiv.org
- num_pde_fub.pdfwias-berlin.de
- [2605.01172] A Theory of Generalization in Deep Learningarxiv.org
- [1707.01415] Machine Learning, Deepest Learning: Statistical Data Assimilation Problemsarxiv.org
- 1806.07366arxiv.org
- [2404.07200] Toward a Better Understanding of Fourier Neural Operators from a Spectral Perspectivearxiv.org
- Statistical Mechanics of Deep Learningganguli-gang.stanford.edu
- MSR-TR-2009-192.pdfmicrosoft.com
- Hamiltonian Neural PDE Solvers through Functional Approximationarxiv.org
- On Degenerate Partial Differential Equationsarxiv.org
- arxiv.org/pdf/1805.08522arxiv.org
- Stochastic Differential Equations, Deep Learning, and High-Dimensional PDEsmitmath.github.io